Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
hash_set = set()
for i in range(1,10**5):
    hash_set.add(i*(i+1)//2)
n = int(input())

if n==1:
    print('NO')
    exit()

i = 1
while True:
    temp = (i * (i+1) // 2 )
    if temp > n:
        print('NO')
        break
    elif (n - temp) in hash_set:
        print('YES')
        break
    i += 1